TSTP Solution File: COM016+1 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : COM016+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:14:33 EDT 2023
% Result : Theorem 2.09s 2.43s
% Output : Proof 2.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM016+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : nanocop.sh %s %d
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 19 03:37:22 EDT 2023
% 0.14/0.34 % CPUTime :
% 2.09/2.43
% 2.09/2.43 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 2.09/2.43 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.09/2.43 %-----------------------------------------------------
% 2.09/2.43 ncf(matrix, plain, [(610 ^ _81635) ^ [_101109] : [aElement0(_101109), aReductOfIn0(_101109, xa, xR), sdtmndtasgtdt0(_101109, xR, xb)], (2 ^ _81635) ^ [_81759] : [-(_81759 = _81759)], (4 ^ _81635) ^ [_81866, _81868] : [_81868 = _81866, -(_81866 = _81868)], (10 ^ _81635) ^ [_82070, _82072, _82074] : [-(_82074 = _82070), _82074 = _82072, _82072 = _82070], (20 ^ _81635) ^ [_82383, _82385] : [-(isConfluent0(_82383)), _82385 = _82383, isConfluent0(_82385)], (30 ^ _81635) ^ [_82734, _82736, _82738, _82740, _82742, _82744] : [-(aNormalFormOfIn0(_82742, _82738, _82734)), aNormalFormOfIn0(_82744, _82740, _82736), _82744 = _82742, _82740 = _82738, _82736 = _82734], (48 ^ _81635) ^ [_83287, _83289] : [-(aRewritingSystem0(_83287)), _83289 = _83287, aRewritingSystem0(_83289)], (58 ^ _81635) ^ [_83582, _83584] : [-(isLocallyConfluent0(_83582)), _83584 = _83582, isLocallyConfluent0(_83584)], (68 ^ _81635) ^ [_83877, _83879] : [-(isTerminating0(_83877)), _83879 = _83877, isTerminating0(_83879)], (78 ^ _81635) ^ [_84200, _84202, _84204, _84206] : [-(iLess0(_84204, _84200)), iLess0(_84206, _84202), _84206 = _84204, _84202 = _84200], (92 ^ _81635) ^ [_84672, _84674, _84676, _84678, _84680, _84682] : [-(sdtmndtplgtdt0(_84680, _84676, _84672)), sdtmndtplgtdt0(_84682, _84678, _84674), _84682 = _84680, _84678 = _84676, _84674 = _84672], (110 ^ _81635) ^ [_85225, _85227] : [-(aElement0(_85225)), _85227 = _85225, aElement0(_85227)], (120 ^ _81635) ^ [_85576, _85578, _85580, _85582, _85584, _85586] : [-(aReductOfIn0(_85584, _85580, _85576)), aReductOfIn0(_85586, _85582, _85578), _85586 = _85584, _85582 = _85580, _85578 = _85576], (138 ^ _81635) ^ [_86165, _86167, _86169, _86171, _86173, _86175] : [-(sdtmndtasgtdt0(_86173, _86169, _86165)), sdtmndtasgtdt0(_86175, _86171, _86167), _86175 = _86173, _86171 = _86169, _86167 = _86165], (156 ^ _81635) ^ [_86728] : [aElement0(_86728), true___, -(true___)], (166 ^ _81635) ^ [_86983] : [aRewritingSystem0(_86983), true___, -(true___)], (176 ^ _81635) ^ [_87252, _87254] : [aElement0(_87254), aRewritingSystem0(_87252), 183 ^ _81635 : [(184 ^ _81635) ^ [_87474] : [aReductOfIn0(_87474, _87254, _87252), -(aElement0(_87474))]]], (190 ^ _81635) ^ [_87701, _87703] : [aElement0(_87703), aElement0(_87701), iLess0(_87703, _87701), true___, -(true___)], (208 ^ _81635) ^ [_88175, _88177, _88179] : [aElement0(_88179), aRewritingSystem0(_88177), aElement0(_88175), sdtmndtplgtdt0(_88179, _88177, _88175), true___, -(true___)], (230 ^ _81635) ^ [_88762, _88764, _88766] : [aElement0(_88766), aRewritingSystem0(_88764), aElement0(_88762), 241 ^ _81635 : [(242 ^ _81635) ^ [] : [sdtmndtplgtdt0(_88766, _88764, _88762), -(aReductOfIn0(_88762, _88766, _88764)), 250 ^ _81635 : [(251 ^ _81635) ^ [] : [-(aElement0(249 ^ [_88762, _88764, _88766]))], (253 ^ _81635) ^ [] : [-(aReductOfIn0(249 ^ [_88762, _88764, _88766], _88766, _88764))], (255 ^ _81635) ^ [] : [-(sdtmndtplgtdt0(249 ^ [_88762, _88764, _88766], _88764, _88762))]]], (257 ^ _81635) ^ [] : [-(sdtmndtplgtdt0(_88766, _88764, _88762)), 258 ^ _81635 : [(259 ^ _81635) ^ [] : [aReductOfIn0(_88762, _88766, _88764)], (261 ^ _81635) ^ [_89693] : [aElement0(_89693), aReductOfIn0(_89693, _88766, _88764), sdtmndtplgtdt0(_89693, _88764, _88762)]]]]], (273 ^ _81635) ^ [_90114, _90116, _90118, _90120] : [-(sdtmndtplgtdt0(_90120, _90118, _90114)), sdtmndtplgtdt0(_90120, _90118, _90116), sdtmndtplgtdt0(_90116, _90118, _90114), aElement0(_90120), aRewritingSystem0(_90118), aElement0(_90116), aElement0(_90114)], (299 ^ _81635) ^ [_90837, _90839, _90841] : [aElement0(_90841), aRewritingSystem0(_90839), aElement0(_90837), 310 ^ _81635 : [(321 ^ _81635) ^ [] : [322 ^ _81635 : [(323 ^ _81635) ^ [] : [_90841 = _90837], (325 ^ _81635) ^ [] : [sdtmndtplgtdt0(_90841, _90839, _90837)]], -(sdtmndtasgtdt0(_90841, _90839, _90837))], (311 ^ _81635) ^ [] : [sdtmndtasgtdt0(_90841, _90839, _90837), -(_90841 = _90837), -(sdtmndtplgtdt0(_90841, _90839, _90837))]]], (329 ^ _81635) ^ [_91695, _91697, _91699, _91701] : [-(sdtmndtasgtdt0(_91701, _91699, _91695)), sdtmndtasgtdt0(_91701, _91699, _91697), sdtmndtasgtdt0(_91697, _91699, _91695), aElement0(_91701), aRewritingSystem0(_91699), aElement0(_91697), aElement0(_91695)], (355 ^ _81635) ^ [_92390] : [aRewritingSystem0(_92390), 358 ^ _81635 : [(390 ^ _81635) ^ [] : [-(isConfluent0(_92390)), 394 ^ _81635 : [(395 ^ _81635) ^ [] : [-(aElement0(391 ^ [_92390]))], (397 ^ _81635) ^ [] : [-(aElement0(392 ^ [_92390]))], (399 ^ _81635) ^ [] : [-(aElement0(393 ^ [_92390]))], (401 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_92390], _92390, 392 ^ [_92390]))], (403 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_92390], _92390, 393 ^ [_92390]))], (405 ^ _81635) ^ [_94270] : [aElement0(_94270), sdtmndtasgtdt0(392 ^ [_92390], _92390, _94270), sdtmndtasgtdt0(393 ^ [_92390], _92390, _94270)]]], (359 ^ _81635) ^ [] : [isConfluent0(_92390), 362 ^ _81635 : [(363 ^ _81635) ^ [_92708, _92710, _92712] : [383 ^ _81635 : [(384 ^ _81635) ^ [] : [-(aElement0(382 ^ [_92390, _92708, _92710, _92712]))], (386 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(_92710, _92390, 382 ^ [_92390, _92708, _92710, _92712]))], (388 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(_92708, _92390, 382 ^ [_92390, _92708, _92710, _92712]))]], aElement0(_92712), aElement0(_92710), aElement0(_92708), sdtmndtasgtdt0(_92712, _92390, _92710), sdtmndtasgtdt0(_92712, _92390, _92708)]]]]], (417 ^ _81635) ^ [_94643] : [aRewritingSystem0(_94643), 420 ^ _81635 : [(452 ^ _81635) ^ [] : [-(isLocallyConfluent0(_94643)), 456 ^ _81635 : [(457 ^ _81635) ^ [] : [-(aElement0(453 ^ [_94643]))], (459 ^ _81635) ^ [] : [-(aElement0(454 ^ [_94643]))], (461 ^ _81635) ^ [] : [-(aElement0(455 ^ [_94643]))], (463 ^ _81635) ^ [] : [-(aReductOfIn0(454 ^ [_94643], 453 ^ [_94643], _94643))], (465 ^ _81635) ^ [] : [-(aReductOfIn0(455 ^ [_94643], 453 ^ [_94643], _94643))], (467 ^ _81635) ^ [_96523] : [aElement0(_96523), sdtmndtasgtdt0(454 ^ [_94643], _94643, _96523), sdtmndtasgtdt0(455 ^ [_94643], _94643, _96523)]]], (421 ^ _81635) ^ [] : [isLocallyConfluent0(_94643), 424 ^ _81635 : [(425 ^ _81635) ^ [_94961, _94963, _94965] : [445 ^ _81635 : [(446 ^ _81635) ^ [] : [-(aElement0(444 ^ [_94643, _94961, _94963, _94965]))], (448 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(_94963, _94643, 444 ^ [_94643, _94961, _94963, _94965]))], (450 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(_94961, _94643, 444 ^ [_94643, _94961, _94963, _94965]))]], aElement0(_94965), aElement0(_94963), aElement0(_94961), aReductOfIn0(_94963, _94965, _94643), aReductOfIn0(_94961, _94965, _94643)]]]]], (479 ^ _81635) ^ [_96896] : [aRewritingSystem0(_96896), 482 ^ _81635 : [(501 ^ _81635) ^ [] : [504 ^ _81635 : [(505 ^ _81635) ^ [] : [-(aElement0(502 ^ [_96896]))], (507 ^ _81635) ^ [] : [-(aElement0(503 ^ [_96896]))], (509 ^ _81635) ^ [] : [-(sdtmndtplgtdt0(502 ^ [_96896], _96896, 503 ^ [_96896]))], (511 ^ _81635) ^ [] : [iLess0(503 ^ [_96896], 502 ^ [_96896])]], -(isTerminating0(_96896))], (483 ^ _81635) ^ [] : [isTerminating0(_96896), 486 ^ _81635 : [(487 ^ _81635) ^ [_97165, _97167] : [aElement0(_97167), aElement0(_97165), sdtmndtplgtdt0(_97167, _96896, _97165), -(iLess0(_97165, _97167))]]]]], (515 ^ _81635) ^ [_98069, _98071] : [aElement0(_98071), aRewritingSystem0(_98069), 522 ^ _81635 : [(523 ^ _81635) ^ [_98341] : [aNormalFormOfIn0(_98341, _98071, _98069), 526 ^ _81635 : [(527 ^ _81635) ^ [] : [-(aElement0(_98341))], (529 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(_98071, _98069, _98341))], (531 ^ _81635) ^ [_98617] : [aReductOfIn0(_98617, _98341, _98069)]]], (533 ^ _81635) ^ [_98692] : [-(aNormalFormOfIn0(_98692, _98071, _98069)), aElement0(_98692), sdtmndtasgtdt0(_98071, _98069, _98692), -(aReductOfIn0(542 ^ [_98069, _98071, _98692], _98692, _98069))]]], (548 ^ _81635) ^ [_99164] : [aRewritingSystem0(_99164), isTerminating0(_99164), 555 ^ _81635 : [(556 ^ _81635) ^ [_99383] : [aElement0(_99383), -(aNormalFormOfIn0(559 ^ [_99164, _99383], _99383, _99164))]]], (563 ^ _81635) ^ [] : [-(aRewritingSystem0(xR))], (565 ^ _81635) ^ [] : [-(isLocallyConfluent0(xR))], (567 ^ _81635) ^ [] : [-(isTerminating0(xR))], (569 ^ _81635) ^ [] : [-(aElement0(xa))], (571 ^ _81635) ^ [] : [-(aElement0(xb))], (573 ^ _81635) ^ [] : [-(aElement0(xc))], (606 ^ _81635) ^ [] : [-(sdtmndtplgtdt0(xa, xR, xb))], (608 ^ _81635) ^ [] : [-(sdtmndtplgtdt0(xa, xR, xc))], (575 ^ _81635) ^ [_99998, _100000, _100002] : [iLess0(_100002, xa), 599 ^ _81635 : [(600 ^ _81635) ^ [] : [-(aElement0(598 ^ [_99998, _100000, _100002]))], (602 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(_100000, xR, 598 ^ [_99998, _100000, _100002]))], (604 ^ _81635) ^ [] : [-(sdtmndtasgtdt0(_99998, xR, 598 ^ [_99998, _100000, _100002]))]], aElement0(_100002), aElement0(_100000), aElement0(_99998), sdtmndtasgtdt0(_100002, xR, _100000), sdtmndtasgtdt0(_100002, xR, _99998)]], input).
% 2.09/2.43 ncf('1',plain,[aElement0(249 ^ [xb, xR, xa]), aReductOfIn0(249 ^ [xb, xR, xa], xa, xR), sdtmndtasgtdt0(249 ^ [xb, xR, xa], xR, xb)],start(610 ^ 0,bind([[_101109], [249 ^ [xb, xR, xa]]]))).
% 2.09/2.43 ncf('1.1',plain,[-(aElement0(249 ^ [xb, xR, xa])), 184 : aReductOfIn0(249 ^ [xb, xR, xa], xa, xR), 184 : aElement0(xa), 184 : aRewritingSystem0(xR)],extension(176 ^ 1,bind([[_87252, _87254, _87474], [xR, xa, 249 ^ [xb, xR, xa]]]))).
% 2.09/2.43 ncf('1.1.1',plain,[-(aReductOfIn0(249 ^ [xb, xR, xa], xa, xR)), 242 : sdtmndtplgtdt0(xa, xR, xb), 242 : -(aReductOfIn0(xb, xa, xR)), 242 : aElement0(xa), 242 : aRewritingSystem0(xR), 242 : aElement0(xb)],extension(230 ^ 4,bind([[_88762, _88764, _88766], [xb, xR, xa]]))).
% 2.09/2.43 ncf('1.1.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb)), sdtmndtplgtdt0(xa, xR, xb), xa = xa, xR = xR, xb = xb],extension(92 ^ 7,bind([[_84672, _84674, _84676, _84678, _84680, _84682], [xb, xb, xR, xR, xa, xa]]))).
% 2.09/2.43 ncf('1.1.1.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb)), sdtmndtplgtdt0(xa, xR, xb), xa = xa, xR = xR, xb = xb],extension(92 ^ 8,bind([[_84672, _84674, _84676, _84678, _84680, _84682], [xb, xb, xR, xR, xa, xa]]))).
% 2.09/2.43 ncf('1.1.1.1.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb))],extension(606 ^ 9)).
% 2.09/2.43 ncf('1.1.1.1.1.2',plain,[-(xa = xa)],extension(2 ^ 9,bind([[_81759], [xa]]))).
% 2.09/2.43 ncf('1.1.1.1.1.3',plain,[-(xR = xR)],extension(2 ^ 9,bind([[_81759], [xR]]))).
% 2.09/2.43 ncf('1.1.1.1.1.4',plain,[-(xb = xb)],extension(2 ^ 9,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.1.1.1.2',plain,[-(xa = xa)],extension(2 ^ 8,bind([[_81759], [xa]]))).
% 2.09/2.43 ncf('1.1.1.1.3',plain,[-(xR = xR)],extension(2 ^ 8,bind([[_81759], [xR]]))).
% 2.09/2.43 ncf('1.1.1.1.4',plain,[-(xb = xb)],extension(2 ^ 8,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.1.1.2',plain,[aReductOfIn0(xb, xa, xR), aElement0(xb), sdtmndtasgtdt0(xb, xR, xb)],extension(610 ^ 7,bind([[_101109], [xb]]))).
% 2.09/2.43 ncf('1.1.1.2.1',plain,[-(aElement0(xb)), aReductOfIn0(xb, xa, xR)],extension(184 ^ 8,bind([[_87474], [xb]]))).
% 2.09/2.43 ncf('1.1.1.2.1.1',plain,[-(aReductOfIn0(xb, xa, xR))],reduction('1.1.1')).
% 2.09/2.43 ncf('1.1.1.2.2',plain,[-(sdtmndtasgtdt0(xb, xR, xb)), 323 : xb = xb, 321 : aElement0(xb), 321 : aRewritingSystem0(xR), 321 : aElement0(xb)],extension(299 ^ 8,bind([[_90837, _90839, _90841], [xb, xR, xb]]))).
% 2.09/2.43 ncf('1.1.1.2.2.1',plain,[-(xb = xb)],extension(2 ^ 13,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.1.1.2.2.2',plain,[-(aElement0(xb))],lemmata('[1, 1, 1].x')).
% 2.09/2.43 ncf('1.1.1.2.2.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 9)).
% 2.09/2.43 ncf('1.1.1.2.2.4',plain,[-(aElement0(xb))],lemmata('[2, 1, 1, 1].x')).
% 2.09/2.43 ncf('1.1.1.3',plain,[-(aElement0(xa))],extension(569 ^ 5)).
% 2.09/2.43 ncf('1.1.1.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 5)).
% 2.09/2.43 ncf('1.1.1.5',plain,[-(aElement0(xb))],extension(571 ^ 5)).
% 2.09/2.43 ncf('1.1.2',plain,[-(aElement0(xa))],extension(569 ^ 2)).
% 2.09/2.43 ncf('1.1.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 2)).
% 2.09/2.43 ncf('1.2',plain,[-(aReductOfIn0(249 ^ [xb, xR, xa], xa, xR)), 242 : sdtmndtplgtdt0(xa, xR, xb), 242 : -(aReductOfIn0(xb, xa, xR)), 242 : aElement0(xa), 242 : aRewritingSystem0(xR), 242 : aElement0(xb)],extension(230 ^ 1,bind([[_88762, _88764, _88766], [xb, xR, xa]]))).
% 2.09/2.43 ncf('1.2.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb)), sdtmndtplgtdt0(xa, xR, xb), xa = xa, xR = xR, xb = xb],extension(92 ^ 4,bind([[_84672, _84674, _84676, _84678, _84680, _84682], [xb, xb, xR, xR, xa, xa]]))).
% 2.09/2.43 ncf('1.2.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb)), sdtmndtplgtdt0(xa, xR, xb), xa = xa, xR = xR, xb = xb],extension(92 ^ 5,bind([[_84672, _84674, _84676, _84678, _84680, _84682], [xb, xb, xR, xR, xa, xa]]))).
% 2.09/2.43 ncf('1.2.1.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb)), sdtmndtplgtdt0(xa, xR, xb), xa = xa, xR = xR, xb = xb],extension(92 ^ 6,bind([[_84672, _84674, _84676, _84678, _84680, _84682], [xb, xb, xR, xR, xa, xa]]))).
% 2.09/2.43 ncf('1.2.1.1.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb))],extension(606 ^ 7)).
% 2.09/2.43 ncf('1.2.1.1.1.2',plain,[-(xa = xa)],extension(2 ^ 7,bind([[_81759], [xa]]))).
% 2.09/2.43 ncf('1.2.1.1.1.3',plain,[-(xR = xR)],extension(2 ^ 7,bind([[_81759], [xR]]))).
% 2.09/2.43 ncf('1.2.1.1.1.4',plain,[-(xb = xb)],extension(2 ^ 7,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.2.1.1.2',plain,[-(xa = xa)],extension(2 ^ 6,bind([[_81759], [xa]]))).
% 2.09/2.43 ncf('1.2.1.1.3',plain,[-(xR = xR)],extension(2 ^ 6,bind([[_81759], [xR]]))).
% 2.09/2.43 ncf('1.2.1.1.4',plain,[-(xb = xb)],extension(2 ^ 6,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.2.1.2',plain,[-(xa = xa)],extension(2 ^ 5,bind([[_81759], [xa]]))).
% 2.09/2.43 ncf('1.2.1.3',plain,[-(xR = xR)],extension(2 ^ 5,bind([[_81759], [xR]]))).
% 2.09/2.43 ncf('1.2.1.4',plain,[-(xb = xb)],extension(2 ^ 5,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.2.2',plain,[aReductOfIn0(xb, xa, xR), aElement0(xb), sdtmndtasgtdt0(xb, xR, xb)],extension(610 ^ 4,bind([[_101109], [xb]]))).
% 2.09/2.43 ncf('1.2.2.1',plain,[-(aElement0(xb)), 184 : aReductOfIn0(xb, xa, xR), 184 : aElement0(xa), 184 : aRewritingSystem0(xR)],extension(176 ^ 5,bind([[_87252, _87254, _87474], [xR, xa, xb]]))).
% 2.09/2.43 ncf('1.2.2.1.1',plain,[-(aReductOfIn0(xb, xa, xR))],reduction('1.2')).
% 2.09/2.43 ncf('1.2.2.1.2',plain,[-(aElement0(xa))],extension(569 ^ 6)).
% 2.09/2.43 ncf('1.2.2.1.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 6)).
% 2.09/2.43 ncf('1.2.2.2',plain,[-(sdtmndtasgtdt0(xb, xR, xb)), 323 : xb = xb, 321 : aElement0(xb), 321 : aRewritingSystem0(xR), 321 : aElement0(xb)],extension(299 ^ 5,bind([[_90837, _90839, _90841], [xb, xR, xb]]))).
% 2.09/2.43 ncf('1.2.2.2.1',plain,[-(xb = xb)],extension(2 ^ 10,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.2.2.2.2',plain,[-(aElement0(xb))],lemmata('[2, 1].x')).
% 2.09/2.43 ncf('1.2.2.2.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 6)).
% 2.09/2.43 ncf('1.2.2.2.4',plain,[-(aElement0(xb))],lemmata('[2, 2, 1].x')).
% 2.09/2.43 ncf('1.2.3',plain,[-(aElement0(xa))],extension(569 ^ 2)).
% 2.09/2.43 ncf('1.2.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 2)).
% 2.09/2.43 ncf('1.2.5',plain,[-(aElement0(xb))],extension(571 ^ 2)).
% 2.09/2.43 ncf('1.3',plain,[-(sdtmndtasgtdt0(249 ^ [xb, xR, xa], xR, xb)), 325 : sdtmndtplgtdt0(249 ^ [xb, xR, xa], xR, xb), 321 : aElement0(249 ^ [xb, xR, xa]), 321 : aRewritingSystem0(xR), 321 : aElement0(xb)],extension(299 ^ 1,bind([[_90837, _90839, _90841], [xb, xR, 249 ^ [xb, xR, xa]]]))).
% 2.09/2.43 ncf('1.3.1',plain,[-(sdtmndtplgtdt0(249 ^ [xb, xR, xa], xR, xb)), 242 : sdtmndtplgtdt0(xa, xR, xb), 242 : -(aReductOfIn0(xb, xa, xR)), 242 : aElement0(xa), 242 : aRewritingSystem0(xR), 242 : aElement0(xb)],extension(230 ^ 6,bind([[_88762, _88764, _88766], [xb, xR, xa]]))).
% 2.09/2.43 ncf('1.3.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb)), sdtmndtplgtdt0(xa, xR, xb), xa = xa, xR = xR, xb = xb],extension(92 ^ 9,bind([[_84672, _84674, _84676, _84678, _84680, _84682], [xb, xb, xR, xR, xa, xa]]))).
% 2.09/2.43 ncf('1.3.1.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb)), sdtmndtplgtdt0(xa, xR, xb), xa = xa, xR = xR, xb = xb],extension(92 ^ 10,bind([[_84672, _84674, _84676, _84678, _84680, _84682], [xb, xb, xR, xR, xa, xa]]))).
% 2.09/2.43 ncf('1.3.1.1.1.1',plain,[-(sdtmndtplgtdt0(xa, xR, xb))],extension(606 ^ 11)).
% 2.09/2.43 ncf('1.3.1.1.1.2',plain,[-(xa = xa)],extension(2 ^ 11,bind([[_81759], [xa]]))).
% 2.09/2.43 ncf('1.3.1.1.1.3',plain,[-(xR = xR)],extension(2 ^ 11,bind([[_81759], [xR]]))).
% 2.09/2.43 ncf('1.3.1.1.1.4',plain,[-(xb = xb)],extension(2 ^ 11,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.3.1.1.2',plain,[-(xa = xa)],extension(2 ^ 10,bind([[_81759], [xa]]))).
% 2.09/2.43 ncf('1.3.1.1.3',plain,[-(xR = xR)],extension(2 ^ 10,bind([[_81759], [xR]]))).
% 2.09/2.43 ncf('1.3.1.1.4',plain,[-(xb = xb)],extension(2 ^ 10,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.3.1.2',plain,[aReductOfIn0(xb, xa, xR), aElement0(xb), sdtmndtasgtdt0(xb, xR, xb)],extension(610 ^ 9,bind([[_101109], [xb]]))).
% 2.09/2.43 ncf('1.3.1.2.1',plain,[-(aElement0(xb)), 184 : aReductOfIn0(xb, xa, xR), 184 : aElement0(xa), 184 : aRewritingSystem0(xR)],extension(176 ^ 10,bind([[_87252, _87254, _87474], [xR, xa, xb]]))).
% 2.09/2.43 ncf('1.3.1.2.1.1',plain,[-(aReductOfIn0(xb, xa, xR))],reduction('1.3.1')).
% 2.09/2.43 ncf('1.3.1.2.1.2',plain,[-(aElement0(xa))],extension(569 ^ 11)).
% 2.09/2.43 ncf('1.3.1.2.1.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 11)).
% 2.09/2.43 ncf('1.3.1.2.2',plain,[-(sdtmndtasgtdt0(xb, xR, xb)), 323 : xb = xb, 321 : aElement0(xb), 321 : aRewritingSystem0(xR), 321 : aElement0(xb)],extension(299 ^ 10,bind([[_90837, _90839, _90841], [xb, xR, xb]]))).
% 2.09/2.43 ncf('1.3.1.2.2.1',plain,[-(xb = xb)],extension(2 ^ 15,bind([[_81759], [xb]]))).
% 2.09/2.43 ncf('1.3.1.2.2.2',plain,[-(aElement0(xb))],lemmata('[1, 3, 1].x')).
% 2.09/2.43 ncf('1.3.1.2.2.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 11)).
% 2.09/2.43 ncf('1.3.1.2.2.4',plain,[-(aElement0(xb))],lemmata('[2, 1, 3, 1].x')).
% 2.09/2.43 ncf('1.3.1.3',plain,[-(aElement0(xa))],extension(569 ^ 7)).
% 2.09/2.43 ncf('1.3.1.4',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 7)).
% 2.09/2.43 ncf('1.3.1.5',plain,[-(aElement0(xb))],extension(571 ^ 7)).
% 2.09/2.43 ncf('1.3.2',plain,[-(aElement0(249 ^ [xb, xR, xa]))],lemmata('x')).
% 2.09/2.43 ncf('1.3.3',plain,[-(aRewritingSystem0(xR))],extension(563 ^ 2)).
% 2.09/2.43 ncf('1.3.4',plain,[-(aElement0(xb))],extension(571 ^ 2)).
% 2.09/2.43 %-----------------------------------------------------
% 2.09/2.43 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------